Question 714706
a certain number = x
add 5 to a certain number = (x+5)
one third of (add 5 to a certain number) = (1/3)(x+5)
5 subtracted from a the certain number = (x-5)
one half of (5 subtracted from a the certain number) = (1/2)(x-5)<br>
So "one third of the result obtained by adding 5 to a certain numnber is equal to one-half of the result obtained when 5 is subtracted from the number" translates into:
{{{(1/3)(x+5) = (1/2)(x-5)}}}<br>
Now we solve for x. We could start by multiplying out each side but that will involve a lot of fractions. Instead we'll eliminate the the fractions by multiplying both sides of the equation by the lowest common denominator (LCD) of the two denominators. The LCD of 3 and 2 is 6.
{{{6((1/3)(x+5)) = 6((1/2)(x-5))}}}
which simplifies as follows:
{{{2(x+5) = 3(x-5)}}}
{{{2x+10 = 3x-15}}}
With the fractions gone the rest is easy. Subtractin 2x from each side:
{{{10 = x - 15}}}
Adding 15 to each side:
{{{25 = x}}}